An e.m.f. of `15` volt is applied in a circuit containing `5` henry inductance and `10` ohm resistance. The ratio of the current at time `t=oo` and at `t=1` second is

Options

A. `(E^(1//2))`
B. `(e^(2))/(e^(2)-1)`
C. `(1-e^(-1))`
D. `e^(-1)`

Answer

B

Explanation

`i=i_(0)(1-e^(-Rt//L))`
`i_(0)=(E)/(R )` (steady current) when `t=oo`
`i_(oo)=(E)/(R )(1-e^(-oo))=(5)/(10)=1.5`
`i_(1)=1.5(1-e^(-R//L))=1.5(1-e^(2))`
`implies(i_(oo))/(i_(1))(1)/(1-e^(-2))=(e^(2))/(e^(2)-1)`